[scikit-image] robust epipolar geometry estimation with ransac

Thu Mar 22 05:07:49 EDT 2018

Hi,

It seems like OpenCV is computing the point to epipolar line distance (see https://github.com/opencv/opencv/blob/master/modules/calib3d/src/fundam.cpp#L205) while we use the geometrically more meaningful Sampson error (see https://github.com/scikit-image/scikit-image/blob/master/skimage/transform/_geometric.py#L367). They are not equivalent, hence your residual threshold between the two calls is not consistent.

You could implement the point to epipolar line residual yourself by subclassing our FundamentalMatrixTransform.

Cheers,
Johannes

> On Mar 21, 2018, at 11:40 PM, martin sladecek <martin.sladecek at gmail.com> wrote:
> 
> Hi Juan,
> 
> thanks for your response. I can indeed confirm that the fundamental matrix varies as well. Here are the variances for the same experiment as before (after normalization):
> 
>     Scikit-Image variance of fundamental matrix:
>     [[1.462e-11 4.067e-09 3.153e-04]
>      [3.701e-09 2.891e-10 8.637e-06]
>      [2.857e-03 3.343e-05 0.000e+00]]
>     OpenCV variance of fundamental matrix:
>     [[0.000e+00 1.148e-41 0.000e+00]
>      [0.000e+00 0.000e+00 0.000e+00]
>      [2.708e-35 0.000e+00 0.000e+00]]
> 
> 
> It makes sense to me, because the inliers should be calculated based on how well they comply with the epipolar constraint, here represented by the fundamental matrix.
> 
> As for the parameters, I am also uncertain whether they are the same or not.
> I chose the values based on the Fundamental matrix estimation example (in this case the images are already rectified unlike mine), and the OpenCV Epipolar Geometry tutorial.
> 
> http://scikit-image.org/docs/dev/auto_examples/transform/plot_fundamental_matrix.html#sphx-glr-auto-examples-transform-plot-fundamental-matrix-py
> 
> https://docs.opencv.org/3.0-beta/doc/py_tutorials/py_calib3d/py_epipolar_geometry/py_epipolar_geometry.html#epipolar-geometry
> 
> When deciding on the parameters I inspected both the cv2 and skimage APIs:
> 
> https://docs.opencv.org/3.3.1/d9/d0c/group__calib3d.html#ga30ccb52f4e726daa039fd5cb5bf0822b
> 
> http://scikit-image.org/docs/dev/api/skimage.measure.html#ransac
> 
> The OpenCV API is for C++, but the python bindings are autogenerated from it so the parameters should be the same.
> Unfortunately I don't know enough C++ to go through the the code and understand all the differences between the two implementations.
> 
> ~Martin
> 
> On 21/03/18 04:03, Juan Nunez-Iglesias wrote:
>> @Martin, thanks for the ping. I don’t know about other devs but I’m easier to reach here, for sure. =) I added a comment to SO. Having said that I think Stéfan is more experienced with RANSAC. (My experience ends at having attended Stéfan’s tutorial on the topic. =P) But, can you confirm that the fundamental matrix is also varying between runs of skimage?
>> 
>> Generally, I’m concerned about whether the parameters are really the same. I couldn’t find an API reference for cv2 so I couldn’t check for differences. Can you point me to how you set up the cv2 ransac parameters?
>> 
>> Thanks,
>> 
>> Juan.
>> 
>> On 19 Mar 2018, 1:03 PM -0400, martin sladecek <martin.sladecek at gmail.com>, wrote:
>>> Hello,
>>> 
>>> I'm having trouble achieving robust performance with
>>> `skimage.measure.ransac` when estimating fundamental matrix for a pair
>>> of images.
>>> I'm seeing highly varying results with different random seeds when
>>> compared to OpenCV's `findFundamentalMatrix`.
>>> 
>>> I'm running both skimage's and opencv's ransac on the same sets of
>>> keypoints and with (what I'm assuming are) equivalent parameters.
>>> I'm using the same image pair as OpenCV python tutorials
>>> (https://github.com/abidrahmank/OpenCV2-Python-Tutorials/tree/master/data).
>>> 
>>> Here's my demonstration script:
>>> 
>>>     import cv2
>>>     import numpy as np
>>> 
>>>     from skimage import io
>>>     from skimage.measure import ransac
>>>     from skimage.feature import ORB, match_descriptors
>>>     from skimage.transform import FundamentalMatrixTransform
>>> 
>>>     orb = ORB(n_keypoints=500)
>>> 
>>>     img1 = io.imread('images/right.jpg', as_grey=True)
>>>     orb.detect_and_extract(img1)
>>>     kp1 = orb.keypoints
>>>     desc1 = orb.descriptors
>>> 
>>>     img2 = io.imread('images/left.jpg', as_grey=True)
>>>     orb.detect_and_extract(img2)
>>>     kp2 = orb.keypoints
>>>     desc2 = orb.descriptors
>>> 
>>>     matches = match_descriptors(desc1, desc2, metric='hamming',
>>> cross_check=True)
>>>     kp1 = kp1[matches[:, 0]]
>>>     kp2 = kp2[matches[:, 1]]
>>> 
>>>     n_iter = 10
>>>     skimage_inliers = np.empty((n_iter, len(matches)))
>>>     opencv_inliers = skimage_inliers.copy()
>>> 
>>>     for i in range(n_iter):
>>>         fmat, inliers = ransac((kp1, kp2), FundamentalMatrixTransform,
>>>                                min_samples=8, residual_threshold=3,
>>>                                max_trials=5000, stop_probability=0.99,
>>>                                random_state=i)
>>>         skimage_inliers[i, :] = inliers
>>> 
>>>         cv2.setRNGSeed(i)
>>>         fmat, inliers = cv2.findFundamentalMat(kp1, kp2,
>>> method=cv2.FM_RANSAC,
>>>                                                param1=3, param2=0.99)
>>>         opencv_inliers[i, :] = (inliers.ravel() == 1)
>>> 
>>>     skimage_sum_of_vars = np.sum(np.var(skimage_inliers, axis=0))
>>>     opencv_sum_of_vars = np.sum(np.var(opencv_inliers, axis=0))
>>> 
>>>     print(f'Scikit-Image sum of inlier variances:
>>> {skimage_sum_of_vars:>8.3f}')
>>>     print(f'OpenCV sum of inlier variances: {opencv_sum_of_vars:>8.3f}')
>>> 
>>> And the output:
>>> 
>>>     Scikit-Image sum of inlier variances:   13.240
>>>     OpenCV sum of inlier variances:          0.000
>>> 
>>> I use the sum of variances of inliers obtained from different random
>>> seeds as the metric of robustness.
>>> 
>>> I would expect this number to be very close to zero, because truly
>>> robust ransac should converge to the same model independently of it's
>>> random initialization.
>>> 
>>> How can I make skimage's `ransac` behave as robustly as opencv's?
>>> 
>>> Any other tips on this subject would be greatly appreciated.
>>> 
>>> Best regards,
>>> Martin
>>> 
>>> (I originally posted this question on stackoverflow, but I'm not getting
>>> much traction there, so I figured I'd try the mailing list.)
>>> 
>>> https://stackoverflow.com/questions/49342469/robust-epipolar-geometry-estimation-with-scikit-images-ransac
>>> 
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